Optimal. Leaf size=13 \[ x^2-3 x+\log (2 x+3) \]
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Rubi [A] time = 0.010276, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {697} \[ x^2-3 x+\log (2 x+3) \]
Antiderivative was successfully verified.
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Rule 697
Rubi steps
\begin{align*} \int \frac{-7+4 x^2}{3+2 x} \, dx &=\int \left (-3+2 x+\frac{2}{3+2 x}\right ) \, dx\\ &=-3 x+x^2+\log (3+2 x)\\ \end{align*}
Mathematica [A] time = 0.0033279, size = 16, normalized size = 1.23 \[ x^2-3 x+\log (2 x+3)-\frac{27}{4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 14, normalized size = 1.1 \begin{align*} -3\,x+{x}^{2}+\ln \left ( 3+2\,x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.15183, size = 18, normalized size = 1.38 \begin{align*} x^{2} - 3 \, x + \log \left (2 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.22185, size = 35, normalized size = 2.69 \begin{align*} x^{2} - 3 \, x + \log \left (2 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.071488, size = 12, normalized size = 0.92 \begin{align*} x^{2} - 3 x + \log{\left (2 x + 3 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12069, size = 19, normalized size = 1.46 \begin{align*} x^{2} - 3 \, x + \log \left ({\left | 2 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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